Question

Given 3 5a.

a) 15<5a<20
b) 5<5a<10
c) 10<5a<15
d) 0<5a<5

Answer 1

The option is (c)
`\(10 < 5a < 15\).`

Step-by-step explanation:

To determine the correct answer, we can solve the given inequality
`\(3 < 5a\)` by isolating
`\(a\)`. Dividing both sides of the inequality by 5, we get
`\(0.6 < a\).` Now, if we multiply all sides by 5, we have
`\(3 < 5a\)`. Combining this with the original inequality
`\(5a < 20\),` we get
`\(3 < 5a < 20\)`. The correct option that satisfies this compound inequality is (c)
`\(10 < 5a < 15\).` This is because, within this range,
`\(5a\)` falls between 10 and 15, inclusive.

Understanding how to manipulate inequalities and interpret their solutions is crucial in mathematics. In this case, the initial inequality
`\(3 < 5a\)` is transformed into
`\(10 < 5a < 15\)`, making option (c) the correct answer. It's important to note that solving inequalities involves applying the same operations to both sides, and the direction of the inequality sign may change accordingly. In this instance, recognizing the correct range for
`\(5a\)`ensures an accurate interpretation of the solution.

This problem provides an opportunity to reinforce the principles of solving inequalities and selecting the appropriate answer based on mathematical reasoning. The solution space between 10 and 15 reflects the valid range for the expression
`\(5a\)` given the inequality
`\(3 < 5a < 20\).`

So correct option is option.c